Minimum Entropy Production Effect on a Quantum Scale

The discovery of quantized electric conductance by the group of van Wees in 1988 was a major breakthrough in physics. A decade later, the group of Schwab has proven the existence of quantized thermal conductance. Advancing from these and many other aspects of the quantized conductances in other phenomena of nature, the concept of quantized entropy current can be established and it eases the description of a transferred quantized energy package. This might yield a universal transport behavior of the microscopic world. During the transfer of a single energy quantum, hν, between two neighboring domains, the minimum entropy increment is calculated. It is pointed out that the possible existence of the minimal entropy transfer can be formulated. Moreover, as a new result, it is proved that this minimal entropy transfer principle is equivalent to the Lagrangian description of thermodynamics.

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The principle of minimum entropy production and snow structure

Journal of Glaciology ◽

10.3189/172756504781829945 ◽

2004 ◽

Vol 50 (170) ◽

pp. 342-352 ◽

Cited By ~ 3

Author(s):

Perry Bartelt ◽

Othmar Buser

Keyword(s):

Mass Transfer ◽

Temperature Gradient ◽

Entropy Production ◽

Surface Curvature ◽

The State ◽

Temperature Gradients ◽

Curvature Radius ◽

Minimum Entropy ◽

Snow Layer ◽

Minimum Entropy Production

AbstractAn essential problem in snow science is to predict the changing form of ice grains within a snow layer. Present theories are based on the idea that form changes are driven by mass diffusion induced by temperature gradients within the snow cover. This leads to the well-established theory of isothermal- and temperature-gradient metamorphism. Although diffusion theory treats mass transfer, it does not treat the influence of this mass transfer on the form — the curvature radius of the grains and bonds — directly. Empirical relations, based on observations, are additionally required to predict flat or rounded surfaces. In the following, we postulate that metamorphism, the change of ice surface curvature and size, is a process of thermodynamic optimization in which entropy production is minimized. That is, there exists an optimal surface curvature of the ice grains for a given thermodynamic state at which entropy production is stationary. This state is defined by differences in ice and air temperature and vapor pressure across the interfacial boundary layer. The optimal form corresponds to the state of least wasted work, the state of minimum entropy production. We show that temperature gradients produce a thermal non-equilibrium between the ice and air such that, depending on the temperature, flat surfaces are required to mimimize entropy production. When the temperatures of the ice and air are equal, larger curvature radii are found at low temperatures than at high temperatures. Thus, what is known as isothermal metamorphism corresponds to minimum entropy production at equilibrium temperatures, and so-called temperature-gradient metamorphism corresponds to minimum entropy production at none-quilibrium temperatures. The theory is in good agreement with general observations of crystal form development in dry seasonal alpine snow.

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